Related papers: $G_2$-instantons, associative submanifolds, and Fu…

We employ the ADHM method to derive the moduli space of two instantons in U(1) gauge theory on a noncommutative space. We show by an explicit hyperK\"ahler quotient construction that the relative metric of the moduli space of two instantons…

On an oriented, compact, connected, real four-dimensional manifold, $M$, we introduce a topological Lagrangian gauge field theory with a Bogomol'nyi structure that leads to non-singular, finite-Action, stable solutions to the variational…

We consider $G_2$-structures with torsion coupled with $G_2$-instantons, on a compact $7$-dimensional manifold. The coupling is via an equation for $4$-forms which appears in supergravity and generalized geometry, known as the Bianchi…

We study the superpotential induced by Euclidean D3-brane instantons carrying instanton flux, with special emphasis on its significance for the stabilisation of Kahler moduli and Neveu-Schwarz axions in Type IIB orientifolds. Quite…

We consider the six-sphere S^6=G_2/SU(3) and its twistor space Z=G_2/U(2) associated with the SU(3)-structure on S^6. It is shown that a Hermitian Yang-Mills connection (instanton) on a smooth vector bundle over S^6 is equivalent to a flat…

We present ADHM-Nahm data for instantons on the Taub-NUT space and encode these data in terms of Bow Diagrams. We study the moduli spaces of the instantons and present these spaces as finite hyperkahler quotients. As an example, we find an…

In this note we prove that the moduli space of rank $2n$ symplectic instanton bundles on ${\PP^{2n+1}}$, defined from the well known monad condition, is affine. This result was not known even in the case $n=1$, where the real instanton…

We study supergravity instantons sourced by axion (and saxion) fields in the Euclidean $AdS_3\times S^3 \times CY_2$ vacua of IIB supergravity. Such instantons are described by geodesic curves on the moduli space; the timelike geodesics can…

We discuss the behaviour of non-perturbative superpotentials in 4d N=1 type II compactifications (and orientifolds thereof) near lines of marginal stability, where the spectrum of contributing BPS D-brane instantons changes discontinuously.…

We study instanton contributions to the superpotential of local F-theory compactifications which could potentially be used to engineer models of dynamical supersymmetry breaking. These instantons correspond to Euclidean 3-branes which form…

This work is a continuation of the former paper in which principal bundles are given by compact spin toric manifolds and compact connected semisimple Lie groups. In this paper, ambient manifolds are assumed to be compact toric manifolds and…

We study the instanton contributions of N=2 supersymmetric gauge theory and propose that the instanton moduli space is mapped to the moduli space of punctured spheres. Due to the recursive structure of the boundary in the…

In this expository review we discuss various aspects of gauge theory. While the focus is on mathematics, wherever possible we make contact with theoretical high energy physics. Particular emphasis is placed on instantons and monopoles,…

Let $\mathcal{M}$ be a moduli space of polystable rank 2-bundles bundles with fixed determinant (a moduli space of $\mathrm{PU}(2)$-instantons) on a Gauduchon surface with $p_g=0$ and $b_1=1$. We study the holomorphic structure of…

In this note, we revisit some well-known examples of instantons on flat space that were originally discovered in the physics literature. In particular, we explain how the basic instanton on $\mathbb{R}^4$, with its flat hyperkaehler…

We prove that energy minimizing Yang-Mills connections on a compact $G_{2}$-manifold has holonomy equal to $G_{2}$ are $G_{2}$-instantons, subject to an extra condition on the curvature. Furthermore, we show that energy minimizing…

Within the context of finding the initial conditions of the universe we consider gravitational instantons falling into the Bianchi IX classification. That is, a Euclidean four-manifold with a metric that satisfies Einstein's equations with…

We model A_k and D_k asymptotically locally flat gravitational instantons on the moduli spaces of solutions of U(2) Bogomolny equations with prescribed singularities. We study these moduli spaces using Ward correspondence and find their…

We study, using ADHM construction, instanton effects in an ${\CN}=2$ superconformal $Sp(N)$ gauge theory, arising as effective field theory on a system of $N$ D-3-branes near an orientifold 7-plane and 8 D-7-branes in type I' string theory.…

We consider cones over manifolds admitting real Killing spinors and instanton equations on connections on vector bundles over these manifolds. Such cones are manifolds with special (reduced) holonomy. We generalize the scalar ansatz for a…